Improved Chebyshev inequality: new probability bounds with known supremum of PDF

2018/08/31 by Tomohiro Nishiyama, Nishiyama, Tomohiro
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Inequalities and Applications #Methodology (stat.ME) #Multi-Criteria Decision Making #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1808.10770

openalex publication_date 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite mean and variance (covariance matrix). We also show that the similar result holds for specific discrete probability distributions.

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